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Question

Consider the general motion of a wheel of radius 2 m which can be viewed as pure translation with the velocity v and pure rotation about O with angular velocity 5 rad/s. Which of the following is incorrect?


  1. VAO=10^i
  2. VBO=10^j
  3. VCO=10^i
  4. VDO=10^j


Solution

The correct option is D VDO=10^j
As we know,
VPQ=ω×rPQ
So here, VAO=ω×rAO
=5(^k)×2(^j)=10^i


As we can see, the direction of velocity w.r.t O will be in negative x direction.
Similarly
VBO=ω×rBO=5(^k)×2(^i)=(5×2)(^k×^i)
=10 m/s(^j)=10^j
VCO=ω×rCO=5(^k)×2(^j)=10(^k×^j)
=10(^i)(^k×^j=^i)
VDO=ω×rDO=5(^k)×2(^i)=10×(^k×^i)
=10(^j)
[^k×^i=^j]
Hence, option D is incorrect. 

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